spire: DoubleAlgebra vs field is algebra

[Frank T]

A field is a vector space over itself.
The type Double is naturally a field (spire.std.DoubleIsField)
and even more an algebra over itself (spire.std.DoubleAlgebra)
but the following statement gives an error

   val vs: VectorSpace[Double,Double] = DoubleAlgebra

Error: type mismatch;
 found   : spire.std.DoubleAlgebra
 required: spire.algebra.VectorSpace[Double,Double]
  val da :VectorSpace[Double,Double] = DoubleAlgebra
                                  ^    

Proposal: DoubleAlgebra should be a FieldAlgebra,
every field should be a FieldAlgebra:

class FieldIsAlgebra[F](implicit val scalar:Field[F]) extends FieldAlgebra[F,F] {

  override def timesl(r:F, v:F): F = scalar.times(r, v)

  override def negate(x:F): F = scalar.negate(x)

  override val zero: F = scalar.zero

  override def plus(x:F, y:F): F = scalar.plus(x, y)

  override def times(x:F, y:F): F = scalar.times(x, y)
}

implicit def fieldIsAlgebra[F:Field] = new FieldIsAlgebra[F]

And it works for DoubleIsField

 

  val vs: VectorSpace[Double,Double] = fieldIsAlgebra

[Tongfei Chen]

I prefer you write a function 

VectorSpace.trivial[F: Field]: VectorSpace[F, F]

to do this since this is very trivial. Similarly, a monoid of type Monoid[M] is automatically a Ring[M, Int]. I don't think these trivial relations should be encoded into the inheritance of the typeclasses.